Ordinal Ballot Election Practice 2 (2017)

Prepared by:

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451



web page:


For the election below:

i. How many first place votes did A get? did D get? Did C get?

ii. Determine the winner (if there is one) using the methods. If a tie results break the tie in some reasonable way and explain the method used to break the tie.

a. Plurality

b. Condorcet

(As part of your solution draw a digraph which shows who beats whom in a two-way race. Use a directed edge from X to Y if X beats Y in a two-way contest.)

c. Borda count (to find the count for a candidate use the number of candidates below that person on the ordinal ballot)

(as part of your solution construct a pairwise preference matrix.)

d. Sequential run-off

e (Standard) Run-off

f. Borda count sequential run-off

g. Coombs

h. Bucklin

Bucklin works as follow: If no one wins a majority based of the first place votes, look at only first and second place votes, to see if someone now has a majority. Continue until a winner emerges. Note at some point several people may have a majority.

i. Baldwin's method (sequential run-off based on the Borda Count).


Do any of the methods pick the same winner? Will this always happen?

What method do you think is best? Are you bothered by a method that elects someone who gets no first place votes?